The alignment and local motion-correction pipeline proposed in this work consists of four stages. (1) We estimate full-frame (global) shifts for each movie frame. (2) We partition the globally aligned frames into patches and align each patch stack across frames to obtain per-patch shift trajectories. (3) We fit these patch-wise shifts with the 3D spline deformation model introduced here. (4) We refine the spline parameters by optimizing a cross-correlation-based objective, and use the resulting deformation field to warp and sum frames to produce the final motion-corrected micrograph (Figure 2—source data 1). Detailed descriptions of each stage and the spline model are provided below.

During the acquisition of cryo-EM data, various types of sample motion can occur, including BIM and mechanical movement of the sample due to stage instabilities. Correcting for this motion is an important step in obtaining high-resolution 3D reconstructions of the imaged molecules. In this work, we address more complicated patterns of sample motion by separately performing full-frame alignment and local distortion correction due to sample deformation.

For full-frame alignment, we closely follow our previous version of Unblur (Grant and Grigorieff, 2015) using alignment in three iterations with increasing resolution. The shift for each frame is initially determined using the cross-correlation map between the current frame and the sum of all other frames. Given the low electron exposure per frame, single-frame alignment can be susceptible to noise and misalignment. A large B-factor, which can be adjusted by the user, is applied during this step to suppress high-resolution noise. Sample drift due to mechanical instabilities of the cryo stage is expected to be slowly varying in speed and mostly along a fixed direction. This allows the full-frame shifts to be smoothed using a Savitzky-Golay (SG) filter, which effectively models sample drift while preserving molecular features in the image, and without introducing potential image distortions. The full-frame alignment and trajectory smoothing are sufficient in many cases to achieve 3D reconstruction at near-atomic resolution (Grant and Grigorieff, 2015; Oldham et al., 2016; Bartesaghi et al., 2018).

In some cases, the shifts determined for individual frames deviate significantly from the smoothed trajectory. This could be due to noise but may also reflect properties of the sample or stage, and hence these outliers could represent real physical motion of the sample. Therefore, solely relying on the smoothed curves means that the shifts derived from cross-correlation are not directly applied in the correction, even if they represent real physical motion. To allow potential discontinuities in the motion trajectories in our new approach, this smoothing function is optional and is deactivated by default in Unbend. Instead of using the SG-filtered shifts, we compare the raw shifts to the smoothed curve and identify those shifts that deviate by more than 1.5 times the interquartile range (IQR) from the curve. These outlier shifts are further aligned using a B-factor twice that of the initial alignment (the default B-factor for the initial alignment is 1500 Ų). If shifts remain significantly different after this adjustment, we accept them as the true shifts; otherwise, we apply the new shift values. This strategy helps us detect and correct potential misalignments caused by weak signal in individual frames while preserving the information contained in the raw shifts about real sample motion that does not fit a smooth trajectory.

To correct for local sample distortion, patch-based methods are widely utilized. By aligning small patches across the entire micrograph, these methods can accurately capture local motion. Increasing the number of patches and reducing the patch size can not only provide more accurate local information but also limit the amount of signal per patch, leading to noisier alignments. Users can set the patch size and patch numbers based on their preference. In our default settings, to balance these factors, we set a patch size of 1024×1024 pixels when the output pixel size is <0.5 Å, and 512×512 pixels when the output pixel size is between 0.5 and 2.0 Å. For output pixel sizes >2.0 Å, the 512×512 pixel patch size is scaled by a factor equal to the output pixel size and rounded up to the nearest multiple of 16 to maintain computational efficiency.

The default number of patches along the x and y dimensions, denoted as ${NP}_x$ and $N{P}_y$, are determined by rounding up the values of image dimensions divided by patch size. This configuration minimizes overlap between neighboring patches, enabling more accurate capture of local motion. Users may specify fewer patches along each dimension, resulting in larger patches that capture more signal to ensure complete coverage of the micrograph without gaps. Conversely, increasing the number of patches does not reduce their size; instead, it increases the percentage of overlap between adjacent patches, preserving the default patch size to ensure that each patch retains sufficient signal for robust alignment.

Assuming that full-frame alignment has effectively removed the average motion in each frame, the residual motion detected by patch alignment is primarily attributed to beam-induced sample distortion. We therefore approximate the shifts determined for a given patch across movie frames (a patch stack) as a smooth trajectory. For each patch stack, the alignment is first estimated by calculating the cross-correlation between an individual frame and the average of all other frames, after which the shift trajectory is smoothed using an SG filter.

To identify patches with unreasonable shift sets $\left\{(x_{pi,fi},y_{pi,fi})|f_i\in \left\{1,2,\dots ,NF\right\}\right\}$, where $NF$ is the total number of frames, $pi$ denotes the patch stack, and $x_{pi,fi}$ and $y_{pi,fi}$ represent the shift amounts along the $x$ and $y$ axes for frame $fi$ in patch stack $pi$. We calculate the standard deviation of the shift differences between neighboring frames:

where

Outliers in the set $\left\{{\sigma }_{fi}\left(pi\right)\mid pi\in \left\{1,2,\dots ,NP\right\}\right\}$, with $NP={NP}_x\times {NP}_y$ as the total number of patches, are detected using the 1.5×IQR upper bound criterion. Outlier shifts are then replaced with the shift sets from their nearest-neighbor patches. This procedure effectively detects potential misalignments caused by low signal in individual patches and provides a robust initialization for the subsequent modeling of sample distortion.

Patch-wise shifts, $\left\{\left(x_{pi,fi},y_{pi,fi}\right)\mid pi\in \left\{1,2,\dots ,NP\right\},fi\in \left\{1,2,\dots ,NF\right\}\right\}$, represent motion at the patch centers. To generate a distortion-corrected micrograph, these center shifts must be interpolated to obtain the shifts of every pixel in each movie frame. This requires an interpolation model, for which we employ spline functions to describe the pixel-wise shift distribution across the frames.

Control points and knots

Each cubic B-spline curve segment is defined by four control points, with each control point influencing up to four adjacent segments, whereas each bicubic B-spline surface requires 16 control points. As shown in Figure 1a, control points are not located directly on the curve. The endpoints of curve segments and the four corners of the surface segments are referred to as ‘knots’. Adjusting the control points alters the curve’s shape, while the knots of a uniform spline are evenly distributed. To determine a B-spline curve/surface, we only need to know the knot parameters. The relationship between control points and knots for a curve or surface segment can be expressed as (Agrapart and Batailly, 2020):

(8) ${\displaystyle {\displaystyle K=\frac{1}{6}\mathrm{\Phi }Q(\text{curve}),K=\frac{1}{36}\mathrm{\Phi }(\text{surface}),}}$

Figure 1

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where Φ is the passing matrix determined by the Cox-de Boor algorithm and the chosen boundary conditions. In this work, we adopt free-end boundary conditions, allowing the spline to extend linearly beyond the boundary points (Figure 1b). This prevents artificial curvature at the edges, maintaining the natural flow of the surface without imposing strict derivative constraints. For a cubic spline, the free-end boundary condition is implemented as follows:

(9) ${\displaystyle {\displaystyle Q_{k-1}-2Q_k+Q_{k+1}=0,k\in \left\{2,n+1\right\},}}$

and for bicubic splines, the same condition applies along the edges. At the corners, the boundary condition is:

(10) ${\displaystyle {\displaystyle Q_{k-1,l-1}-2Q_{k,l}+Q_{k+1,l+1}=0,k\in \left\{2,n+1\right\},l\in \left\{2,m+1\right\},}}$

where $m$ and $n$ are the number of knots along $x$ and $y$ axes, respectively.

Knot grid configuration

Our model assigns ${NK}_x$, ${NK}_y$, and ${NK}_z$ as the number of knots along the $x$, $y$, and $z$ axes, respectively. By default, ${NK}_x$ and ${NK}_y$ are set to two-thirds of the patch number in each dimension, with a minimum of four knots, and evenly distributed along $x$ and $y$. Along the $z$ axis, knots are spaced at every 4 e^–/Ų of exposure, forming a 3D grid together with the knots along $x$ and $y$. Since shifts occur in both $x$ and $y$, we maintain two sets of knot parameters, $K_x$ and $K_y$. Given these knots, we can interpolate a dense field of shifts for every pixel in each movie frame, thereby correcting local distortion in each frame.

Figure 2 illustrates the knot grid and the construction of the 3D spline model. In Figure 2a, the spline curve for shifts along the $x$ direction is shown along the exposure accumulation direction. In this case, for a movie with 40 frames and a total exposure of 16 e^–/Ų, a knot is assigned every 10 frames. Once the shift amounts at the knots are determined, the cubic spline model, as described above, is used to compute the shift along $x$ for each movie frame. By combining these shifts with the shifts along the $y$-direction, we can obtain the full spline curve thread as shown in Figure 2b. For a model with ${NK}_x$, ${NK}_y$ knots along $x$ and $y$, we will generate ${NK}_x\times {NK}_y$ of such 3D splines. Thus, for each movie frame, we will have a 2D grid of knots for generating the bicubic spline surface, represented by the black points in Figure 2e. Figure 2c and d shows the shift fields along $x$ and $y$, respectively, for a single movie frame derived using the bicubic splines. Figure 2e displays the image before (gray grid) and after (cyan grid) warping, based on the shift fields shown in Figure 2c and d. For better visualization, we amplified the distortion in these figures.

Figure 2

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Figure 2—source data 1

Unbend movie alignment and local motion correction algorithm.

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2DTM was originally developed to identify biomolecules in images of crowded cellular environments with high precision in both location and orientation. The true-positive detection is based on the 2DTM SNR at each target site (Rickgauer et al., 2017; Sigworth, 2004). More specifically, at each image location $p$, we compute cross-correlation values $CC(p,t)$ between the micrograph and the template over all sampled orientations $t$. We then convert these values to z-scores per location $z\left(p,t\right)$, using the mean and standard deviation of $\left\{CC(p,t{)}_t\right\}$ across orientations:

where ${\mu }_p$ and ${\sigma }_p$ are the mean and standard deviation of the cross-correlation values across orientations at location $p$, respectively. The 2DTM SNR is then defined as the maximum z-score:

A detection is called when $SNR\left(p\right)$ exceeds a threshold $z_{th}$, which is determined based on the complementary error function $r_f=\frac{1}{2}erfc\left(\frac{z_{th}}{\sqrt{2}}\right)$, where the expected false positive rate $r_f$ is calculated by assuming there is one false positive detection (1-FP criterion).

Because the 2DTM SNR is computed by correlating template projections with the micrograph, it provides an unbiased measure of how effective the molecular signal is preserved in the distortion-corrected micrograph. In the present study, we will use both the number of detectable particles and their 2DTM SNR as metrics for evaluating the performance of our distortion correction method.

We applied our model to a range of in situ samples commonly studied in structural biology, including whole cells (bacteria and the edges of mammalian cells), lamellae (yeast and mammalian cells), and cellular lysate. Ribosomes, which can be detected with high accuracy by 2DTM using cisTEM (Grant et al., 2018), were chosen as the primary targets in the following experiments. Furthermore, we also tested the performance of our new algorithm on DeCo-LACE micrograph montages (Elferich et al., 2022).

Using the new graphical user interface (GUI) for motion correction in cisTEM, users can readily visualize local motion by enabling the trajectory option. Figure 3 illustrates an example micrograph acquired from Mycoplasma pneumoniae whole-cell samples. In this case, a vortex-shaped motion is observed in the region where two cells are closely adjacent to each other. This type of spatially varying, non-rigid deformation would not be well captured by simple, low-order global models, while the use of a continuous 3D spline representation in this work can interpolate smoothly across both space and time. The patch trajectories (shown in red) are magnified by a factor of 30 for clarity. Figure 3b and c provides zoomed-in views of the boxed area and the corresponding power spectra generated from the micrograph after local distortion-corrected alignment versus full-frame alignment, respectively. For movies exhibiting the highest estimated motion in each sample type in this work, the recovery of Thon rings at higher spatial frequencies is more apparent (see Figure 4—figure supplements 1–5). Figure 3d and e shows the detected particles (white projections) using 2DTM in the micrograph processed with and without local distortion correction, respectively. The larger number of detected 2DTM targets demonstrates that the blurring caused by the local distortion has been significantly reduced by our Unbend program. This can also be seen in the power spectra calculated from the micrograph, exhibiting more pronounced Thon rings at higher resolution after local distortion correction (Figure 3b and c).

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We benchmarked our motion-correction model using three types of in situ specimens: whole cells, lamellae, and cell lysates. For whole cells, we used a frozen-hydrated M. pneumoniae dataset (O’Reilly et al., 2020) previously employed for the development of 2DTM with cisTEM (Lucas et al., 2021). To enable comparison across different sample types and geometries, mammalian cells were also included; specifically, immortalized Cercopithecus aethiops (African green monkey) BS-C-1 kidney epithelial cells (see Materials and methods). Lamella datasets originated from two eukaryotic organisms – Saccharomyces cerevisiae and immortalized Mus musculus ER-HoxB8 cells – both previously analyzed by 2DTM (Lucas et al., 2022; Elferich et al., 2022). The cell lysate sample was derived from BS-C-1 cells, as described in Materials and methods.

To quantify the local movement, we measure the displacement of each patch’s last frame relative to its first frame in a micrograph $\left\{s{h}_{pi}\mid pi\in \left\{1,2,\dots ,NP\right\}\right\}$, where

Since the full-frame alignment is assumed to remove the global average motion, the patch motions/shifts (${sh}_{pi}$) primarily represent the BIM that reflect the sample’s deformation, measuring how much the patch centers are displaced from their initial positions. To characterize the extent of local motion, we compute the maximum, mean, and standard deviation of these shifts for each micrograph. We find that cell lysate exhibits the least local motion, whereas the M. pneumoniae samples demonstrate substantially larger local motions, with maximum displacements of over 55 Å. M. musculus cell lamella, and BS-C-1 cell edge samples also show considerable local motion (up to 20 Å). As indicated by the standard deviation data in Figure 4, samples with large average patch motion also exhibit greater variability in local motion across a micrograph. Such pronounced local motion will significantly attenuate high-resolution information in the micrograph, making its correction essential for high-resolution cryo-EM experiments.

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Figure 4—source data 1

Summary statistics of per-micrograph mean patch shifts by sample type.

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Figure 4—source data 2

Motion and equivalent strain summary table for micrographs shown in Figure 4—figure supplements 1–5.

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To assess whether local motion correlates with specimen thickness, we estimated the sample thickness using CTFFIND5 (Elferich et al., 2024) and plotted the mean shift against sample thickness for each micrograph (Figure 4b). For consistency, all micrographs were binned to 1.5 Å/pixel during alignment, and outliers shown in Figure 4a are excluded for better pattern visualization. BS-C-1 cell edge samples span a broad thickness range (50–400 nm), and their mean displacements likewise cover the full range of observed shifts. M. pneumoniae are generally thicker (150–400 nm), and their mean displacements also distribute in the upper range (2.5–6 Å). In contrast, cell-lysate specimens are thinner (50–150 nm) and exhibit the least local motion, and even at the upper end (100–150 nm) of this range exhibit mean shifts below 1 Å. However, lamellae of similar thickness show mean displacements from <1 to >6 Å. These results indicate no direct dependence of local motion on sample thickness; rather, motion magnitude is highly related to the sample type and preparation method.

To quantify pixel-wise shifts within each movie frame, we developed shift_field_generation, a program that reconstructs the per-pixel displacement field of any given frame by interpolating the spline parameters exported by Unbend during movie alignment. Using the first frame as a reference, we compute the displacement of the final frame and derive two complementary strain measures: Von Mises equivalent strain, which measures distortional (shape-changing) effects, and total equivalent strain, which captures both volumetric (area-changing) and distortional components (see Materials and methods). Both measures range from 0 to infinite, with 0 designating no deformation, and provide scalar quantities that condense a multidimensional strain (or stress) state to equivalent single-dimensional values.

Figure 5 presents strain maps (per pixel) for the example micrograph shown in Figure 3. The Von Mises (Green-Lagrange strain) map (Figure 5a) highlights a localized shear-dominated ‘vortex’ region where strain exceeds 1%, indicating significant non-isotropic deformation, which is consistent with the rotation motion shown by the patch trajectories in Figure 3a. The total equivalent strain map (Figure 5b) shows that the total equivalent strain in this area is above 1.4%, with the rest of the field remaining below 1.2% deformation.

Figure 5

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The result in Figure 5 is based on the alignment using a grid of 12×8 patches, which can track the local strain patterns with fine granularity. Reducing the number of patches can smooth small-scale fluctuations and reduce apparent peak strain values, but may under-sample genuine local distortions. This trade-off between patch resolution and deformation magnitude suggests that the optimal patch density may depend on sample type and exposure rate. Unbend allows users to tailor the number of patches to their specimen and exposure-fractionation scheme, optimizing alignment fidelity and desired amount of deformation correction.

To assess improvements in preserving high-resolution signal in the motion-corrected micrographs, we searched for large ribosomal subunits (LSUs) using 2DTM, as described in the Materials and methods section. Stronger high-resolution signal leads to both an increased number of detected targets (Figure 6a) and higher 2DTM SNR values (Figure 6b). We also compared the SNRs of the same detections present in both micrographs processed with full-frame alignment and those processed with local distortion correction. The SNR differences are shown in Figure 6c, sorted for better visualization.

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In whole-cell M. pneumoniae samples, distortion correction resulted in a 4.2-fold increase in LSU detection (95.5 vs 22.9 detections per image), and the mean 2DTM SNR improved by ~3.1% (8.96±0.02 vs 8.69±0.01). The low values of standard error of the mean (SEM) (0.02 and 0.01) indicate a consistent 2DTM SNR improvement. In BS-C-1 whole-cell samples, the number of LSU detections increased from 55.9 to 69.1 (~23.6% improvement), and the 2DTM SNR improved from 9.88±0.02 to 10.42±0.02 (~5.5% improvement). For targets detected in both full-frame and local-distortion corrected micrographs, approximately 80% showed higher 2DTM SNR values after local distortion correction (Figure 6c). Of the 20% of detected targets that displayed lower 2DTM SNR values after local distortion correction, some showed a reduction of up to a factor of 2. This reduction can be attributed to the motion correction process, which optimizes an overall loss function $L_2\left(K_x,K_y\right)$ and models motion using continuous functions to avoid patch alignments dominated by noise. This suggests that there are local areas that happen to be well aligned using full-frame alignment, and that end up with an overall worse alignment when additional degrees of freedom are added during local alignment. Nevertheless, local distortion correction resulted in a 317% increase in LSU detections in M. pneumoniae and a 24% increase for BS-C-1, with an overall 2DTM SNR improvement of 3–5%.

For lamellae prepared from S. cerevisiae and ER-HoxB8 cells, the mean number of LSU detections per micrograph increased from 350 to 401 (~15% increase) in yeast samples and from 8.5 to 10.0 (~17% increase) in mammalian samples. The mean 2DTM SNR for yeast samples improved from 10.18±0.01 to 10.62±0.01 (~4% increase), and for mammalian samples, it increased from 10.4±0.1 to 11.2±0.1 (~8% increase). As noted earlier, motion in ER-HoxB8 lamellae varies from less than 1 to 6 Å, contributing to a relatively larger SEM value (0.1).

Lysates generated from BS-C-1 cells showed no substantial increase in the number of LSU detections, but a 3% improvement in the 2DTM SNR was observed (from 13.84±0.04 to 14.25±0.04). As shown in Figure 4, cell lysates exhibit minimal local motion (mean shift amount 0.7 Å, Figure 4—source data 1), and full-frame alignment is sufficient to correct for most BIM in these samples. However, small amounts of local motion may remain, and this may explain the improved 2DTM SNR in 70% of the detected targets (Figure 6c).

To better understand the beam-induced deformations, we analyzed a dataset of micrographs collected from lamellae of Candida albicans cells (Serrano et al., 2026). In this dataset, lamellae of individual cells were imaged as montages (DeCo-LACE, Elferich et al., 2022). We performed motion correction of the individual exposures within these montages using either full-frame alignment or Unbend, and found that in 47 out of 82 montages, the number of detected targets increased by more than 10% (Figure 7a). This indicates that patch-based motion correction recovered signal that would otherwise have been lost to image blurring due to local deformations. In some montages, the number of detected targets was substantially higher in every exposure (Figure 7c), suggesting that these regions of the imaged lamella were generally prone to local deformations and the observed increase in the number of detected targets was not due to a few heavily distorted exposures.

Figure 7

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For the remaining 35 montages that showed less than a 10% increase in target detection, the number of detections remained approximately unchanged between full-frame and local-distortion correction (Figure 7b). While we cannot rule out that areas in these lamellae experienced local deformations that were not corrected by our algorithm, the overall similarity in the number of detections per exposure and in the 2DTM SNR of 60S targets compared to the full dataset suggests that these areas likely did not suffer from significant BIM. In fact, the mean 2DTM SNR in areas with less than a 10% increase in detections was 11.1, whereas the mean 2DTM SNR in areas with more than a 50% increase was 10.7. This suggests that patch-based motion correction recovers most, but not all, signal lost to local deformation.

In summary, our data suggest that local deformation in lamellae is not uniform: for reasons that remain unclear, some lamellae remain rigid while others display local deformation. Together with the finding that, despite patch-based motion correction, the average 2DTM SNR is still higher in areas without deformation, we propose that future work aimed at uncovering the physical basis of this variability could lead to improvements in in situ cryo-EM datasets.

Several other movie alignment pipelines implement local motion correction using different deformation models. Widely used approaches include (1) quadratic (low-order polynomial) motion models, as implemented in MotionCor2/MotionCor3 (Zheng et al., 2017), and (2) spline-based models that allow more flexible deformation fields, as implemented in Warp (Tegunov and Cramer, 2019) and CryoSPARC (Punjani et al., 2017).

In this section, we performed movie alignment using five methods (Unbend, MotionCor2, MotionCor3, Warp, and CryoSPARC) and then ran 2DTM on the resulting motion-corrected micrographs. Because several packages only support downsampling by integer factors and all movies were recorded at super-resolution, the aligned outputs were either not binned or binned by a factor of 2. To standardize sampling across methods and samples for downstream analysis, we then Fourier-binned the corrected micrographs to a final pixel size of 1.5 Å/pixel. For Unbend, all alignment parameters were kept at their default values. For the other packages, we matched the nominal model flexibility to Unbend’s model by using the same number of patches along x and y in MotionCor2 and MotionCor3, and the same number of spline knots in Warp and CryoSPARC. All remaining parameters were left at their respective defaults to minimize method-specific tuning and reduce potential bias.

Figure 8a summarizes the number of 2DTM detections per micrograph for each motion-correction method. For particles detected by both Unbend and an alternative method, we computed the SNR difference as $\mathrm{\Delta }SNR=SN{R}_{Unbend}-SN{R}_{other}$. The sorted $∆SNR$ distributions are shown in Figure 8b.

Figure 8

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Statistics table for detected particles from micrographs processed by different software.

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For the M. pneumoniae sample, which exhibits the largest local motion (Figure 4a), Unbend produced the highest detection rate, with a mean of 79.7 detections per micrograph, followed by MotionCor2 (70.6). In contrast, CryoSPARC produced 50.4 detections per micrograph, 36.8% fewer than Unbend. Consistent with this, among particles detected by both Unbend and Warp, over 60% had higher SNR in the Unbend-corrected micrographs.

For the cell edge sample, where the mean patch shift spans from <1 to >5 Å (Figure 4b), the mean detection counts between different methods are more similar than in the bacterial sample. However, the SNR comparison (Figure 8b) shows a clear advantage for Unbend: more than 70% of commonly detected particles have higher SNR in Unbend-processed micrographs than in micrographs processed by the other methods, indicating improved recovery of local signal.

For the yeast lamella sample, performance is more consistent between methods. Considering the SNR of commonly detected particles, CryoSPARC performs slightly better than Unbend (only ~44% of common particles show higher SNR in Unbend), MotionCor2 performs similarly to Unbend, and Warp performs slightly worse (with our choice of run parameters). For the mammalian lamella sample, the methods yield similar detection counts (Figure 8a). However, the SNR comparisons favor Unbend: detections from Unbend-processed micrographs show higher 2DTM SNR than all other methods. In particular, Unbend yields higher SNR for ~80% of the particles common with the spline-based methods (Warp and CryoSPARC). For the cell-lysate sample, overlap in detections is high across methods, but 60–70% of commonly detected particles still show higher SNR in the Unbend-corrected micrographs.

Overall, Unbend provides the best and most consistent performance across datasets in our benchmark. MotionCor2 and MotionCor3 perform consistently and robustly across samples, whereas Warp and CryoSPARC show stronger dataset dependence. We aimed to minimize user bias by matching model flexibility and otherwise using default parameters; nevertheless, method-specific parameter optimization could affect absolute performance. A comprehensive, method-specific parameter benchmarking study is beyond the scope of this work.

We benchmarked the runtimes of Unbend using the movie datasets analyzed in this study. Each job was executed with 4 CPU threads on Intel Xeon Gold 5520+ processors. Table 1 summarizes the runtimes together with key parameters of the input movies and the corresponding output micrographs. The runtimes range from ~1.5 to ~12.5 min per movie, depending primarily on the input image size and the number of frames. Unbend is currently CPU-based and therefore slower than the GPU-accelerated implementations. The most time-consuming step is the pixel-wise interpolation, which is performed on unbinned frames. This explains why larger input dimensions and higher frame numbers result in longer runtimes. A GPU-accelerated version of Unbend, as well as additional code-level optimizations to reduce runtime, will be available in a future release.

We validated Unbend across diverse in situ samples, including whole cells, lamellae, and cell lysates, and used 2DTM to quantify the improvement in high-resolution signal in the motion-corrected micrographs. Across all sample types tested, Unbend boosted 2DTM SNR by 3–8% and the number of detected targets by up to 300%, with the largest gains observed in specimens exhibiting large local motion (whole cells and lamellae). While cell lysate showed minimal local motions, a 3% improvement in 2DTM SNR was still observed.

Equivalent strain analysis confirmed that, apart from some samples of the M. pneumoniae dataset, correction-induced deformations remain below 1.0%, suggesting that the model improves alignment without introducing excessive errors. The strain fields showing the maximum patch shift amounts in micrographs of different samples in Figure 4 are presented in Figure 4—figure supplements 1–5 and summarized in Figure 4—source data 2. For the M. pneumoniae sample in Figure 4—figure supplement 1, strain analysis revealed maximum Von Mises and total equivalent values exceeding 2.2% and 3.5%, respectively, consistent with plastic deformation. Comparison of the corresponding power spectra (Figure 4—figure supplement 1a and b) showed that the micrographs corrected with Unbend displayed stronger Thon rings at high spatial frequencies, confirming that the observed plastic deformation was, at least partially, accommodated.

Together, these results demonstrate that local motion correction is essential for obtaining fully motion-corrected micrographs, especially when imaging whole cells and lamellae.

Our results indicate that specimen type and preparation method strongly influence local sample motion. Whole cells often exhibit large thickness gradients that can potentially create areas of differential motion under the electron beam, while in lamellae, which are generally thinner and more homogeneous, some stress may still be present due to the milling process and residual sample inhomogeneity. The local distortion correction model is particularly beneficial in this context, as it can compensate for these localized motion artifacts, leading to more accurate particle detection and improved 2DTM SNR. Cell lysates typically show less localized motion, and full-frame alignment is sufficient for detecting most targets using 2DTM, although some residual local distortion remains detectable and correctable.

Lamellae montages collected using DeCo-LACE (Elferich et al., 2022) further revealed substantial spatial heterogeneity in the amount of local motion, indicated by the range of 2DTM detection gains from under 10% to over 50% within a single sample. We found that montages with less motion better preserve high-resolution signal, suggesting that further improvements in the motion correction model, perhaps based on a more detailed physical mechanism, may yield additional benefits. For single particle samples, which are generally thin and homogeneous, local motion is less pronounced, and full-frame alignment should be sufficient in most cases. Therefore, they were not tested in this work.

Adherent BS-C-1 cells were cultured as previously described by Salgado et al., 2018. Briefly, cells were maintained at 37°C in a humidified atmosphere with 5% CO₂ and grown in Dulbecco’s Modified Eagle Medium (DMEM; Invitrogen) supplemented with 10% fetal bovine serum, 1× GlutaMAX (Thermo Fisher Scientific), and 1% penicillin-streptomycin (100 U/mL penicillin and 100 µg/mL streptomycin; Thermo Fisher Scientific). For grid seeding, cells were washed twice with pre-warmed PBS and detached using trypsin-EDTA (Gibco). Cells were counted, diluted to 1×10⁵ cells/mL and seeded onto fibronectin-coated (5 µg/mL in PBS) EM grids. BS-C-1 cells were obtained from ATCC and used without further authentication or testing for mycoplasma contamination.

Double-side glow-discharged, 200-mesh gold grids with a silicon oxide support film containing 2 µm holes and 2 µm spacing (Quantifoil) were used. Prior to use, grids were cleaned by three washes with ethyl acetate and exposed to UV light under a laminar flow hood for 45 min. Grids were placed into 35 mm glass-bottom tissue culture dishes (MatTek) for cell growth. Cells were allowed to adhere and spread for 24–48 hr before vitrification. Each grid was inspected under an inverted light microscope to confirm appropriate cell density and carbon film integrity. We aimed for approximately one cell per mesh; grids with excessive cell clumping were excluded.

Immediately before plunge freezing, grids were washed twice with warm PBS and transferred into Minimum Essential Medium Eagle Alpha (MEMα; Sigma) supplemented with 25 mM of HEPES buffer. Grids were then rapidly moved from the incubator to a Leica GP2 cryo-plunger; excess liquid was blotted from the back side for 8 s, and grids were plunge-frozen into liquid ethane cooled to –184°C.

Cell extracts were prepared from BSC-1 cells using digitonin-based semi-permeabilization. Briefly, cells were seeded in a 75 cm² flask and cultured to confluence. After washing twice with pre-warmed PBS, the cells were detached with trypsin-EDTA (Gibco) and collected by centrifugation at 300×g for 4 min. The cell pellet was resuspended in 100 μL of semi-permeabilization buffer (25 mM HEPES, 110 mM potassium acetate, 15 mM magnesium acetate, 1 mM DTT, 0.015% digitonin, protease inhibitor cocktail [1 tablet/10 mL; Roche], 40 U/mL RNase In [Promega], 1 mM EGTA) and kept at 4°C for 5 min. Following centrifugation at 1000×g for 5 min, the supernatant was collected for use in grid preparation without further modification. RNA concentration was quantified prior to grid preparation as a quality control measure, with no dilution of the extract performed. Glow-discharged Quantifoil 200-mesh gold grids with a silicon oxide support film containing 2 µm holes and 2 µm spacing were used. Plunge-freezing conditions used were identical to those described for whole cells.

Cryo-EM data were collected using a Titan Krios transmission electron microscope (Thermo Fisher Scientific) operated at 300 keV, equipped with a K3 direct electron detector and an energy filter (Gatan) set to a 20 eV slit width.

For cell edge data collection, medium magnification montages were used to select vitrified cell areas that were transparent enough for cryo-EM. Images were acquired at a nominal magnification of ×64,000 corresponding to a calibrated pixel size of 1.33 Å. A defocus range of –1.0 to –1.5 µm was targeted using SerialEM’s autofocus function (Mastronarde, 2005) on a sacrificial area. Movies were recorded at an exposure rate of 1.02 e^–/Å per frame to a total accumulated exposure of 30.6 e^–/Å.

For the cell lysate, we used a nominal magnification of ×105,000 corresponding to a calibrated pixel size of 0.83 Å. We employed beam tilt to acquire multiple movies (5 per hole across nine holes) at each stage position. Zero-loss peak (ZLP) refinement was performed every 90 min at a unique location to avoid dark areas. Movies containing 30 frames, with an exposure of 1.0 e^–/Å per frame, were recorded, resulting in a total exposure of 30 e^–/Å.

For 2DTM, 3D templates were generated from trimmed atomic models containing only the LSU (50S or 60S), using the simulate program (Himes and Grigorieff, 2021). Specifically, models derived from PDB entries 5LZV (for mammalian samples: BS-C-1 and ER-HoxB8), 6Q8Y (for S. cerevisiae), and 3J9W (for M. pneumoniae) were used. The defocus of the micrographs was determined using CTFFIND5. 2DTM was performed using the match_template program (Lucas et al., 2021) as implemented in cisTEM. The search was conducted with an in-plane angular step of 1.5° and an out-of-plane step of 2.5°. For whole-cell and lamella samples, an additional defocus search was conducted within ±120 nm of the estimated defocus, using 20 nm increments.

Template-matched coordinates, Euler angles, and defocus values were extracted using the MT module within the cisTEM GUI and exported as .star files. These files were subsequently analyzed to quantify the number of detected targets and the 2DTM SNR using a custom Python package (https://github.com/LingliKong/2DTMSNR_MoCo_Bench; copy archived at Kong, 2026). The sample thickness was determined using CTFFIND5.

The Von Mises equivalent strain derives from the Von Mises criterion, widely used in engineering and mechanics to predict yielding or failure of materials subjected to complex (multiaxial) stresses or strains. The Von Mises equivalent strain effectively measures how far a material is distorted from its original shape. In our case, with the shift field $\{u_x,u_y\}$, we can obtain the deformation gradient F:

The Green-Lagrange strain tensor E filters out the rigid-body rotations, measures the true finite strains, and can be calculated by:

The total equivalent strain combines the magnitude of all deformation modes (axial+shear) and is expressed as:

The Von Mises equivalent strain removes the volume change and only keeps the shape change:

where $E_{ij}^{dev}$ is the deviatoric strain:

where ${\delta }_{ij}$ is the Kronecker delta, and $trE$ is the volumetric part/trace, which represents the pure ‘dilation’ or ‘compression’ component that changes the area but not shape:

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

The authors thank members of the Grigorieff lab for helpful discussions. We are also grateful for the use of and support from the cryo-EM facility at UMass Chan Medical School. LK and NG acknowledge funding from the Chan Zuckerberg Initiative, grant #2021-234617(5022).

1. Sent for peer review: September 5, 2025
2. Preprint posted: September 6, 2025
3. Reviewed Preprint version 1: October 31, 2025
4. Reviewed Preprint version 2: April 7, 2026
5. Version of Record published: April 30, 2026

You can cite all versions using the DOI https://doi.org/10.7554/eLife.109119. This DOI represents all versions, and will always resolve to the latest one.

© 2025, Kong et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.